Competing Effects of Buckling and Anchorage Strength on Optimal Wheat Stalk Geometry

Abstract

We seek the ideal wheat stalk, which minimizes the structural mass required to support a fixed grain load in the presence of gravity and wind. The optimization search is restricted to stepped cylindrical stems of known moduli and density but unknown dimension. Stem buckling and root anchorage strength are assumed to place restrictions on the permissible stalk resonant frequency in the presence of a specified wind forcing frequency. These effects are described mathematically, and the penalty parameter method is used to find stem mass minima for various stalk heights. In general, there are two alternative solution branches. The lower solution is the global minimum but it is probably impractical for field crops exposed to natural wind. The upper minimum is more conservative and therefore requires more stem mass. Due to the competing requirements of buckling versus anchorage strength, the parameter study shows that optimal wheat stem geometry has a nonlinear dependence on the intensity of gravity and the frequency spectra of the wind.